Paramount was one of dozens of brands of American chord zithers. I have no idea whether a Paramount is better or worse than any of the other makes.

In general, chord zithers were inexpensive instruments, sold either by mail order or by itinerant salesmen. Many of them have a number under each string, corresponding to "numeric" sheet music intended for people who had no formal musical training and could not read conventional musical notation. You can find some examples of music books for numeric instruments at http://www.geocities.com/~ukelin/songbook.html. The same numeric notation system was also used for other instruments with a million strings, like the ukelin, tremoloa, Marxophone and many others. The modern autoharp is a direct descendent of those things.

This is not a sophisticated instrument. It's certainly possible to make reasonably pleasant music on one of those things (I use thumb picks on my similar "Mandolin Guitar," which is neither a mandolin nor a guitar), but the best thing to do with one of them is probably to clean it up, apply some wood polish and hang it on the wall.